The Blues are said to be determined to boost their defensive options for the 2021-22 campaign, and Kounde has been strongly linked with a switch to Stamford Bridge in recent weeks.
According to AS, the Champions League winners have reached an agreement with the Frenchman on personal terms and must now settle on a transfer fee with his Spanish club.
Sevilla are believed to value their defender, who still has three years left to run on his contract at Estadio Ramon, in the region of €70m (£59.6m), which Chelsea were allegedly not prepared to pay earlier in the window.
The Blues spent just under £100m to bring Romelu Lukaku back to the club this summer, while the club are allegedly weighing up a move for Atletico Madrid midfielder Saul Niguez.
Thomas Tuchel's side will be looking to make it back-to-back wins at the start of the new Premier League season when they travel to Arsenal on Sunday afternoon.